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    <title>H进制用矩阵表示，待求解的方程组</title>

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    <p>根据H进制，用字母A-F表示0-5，设三阶参数矩阵有</p>
    <p>
        $$
        \mathbb{A} =
        \begin{bmatrix}
        A_{0} & A_{1} & A_{2} \\
        A_{3} & A_{4} & A_{5} \\
        A_{6} & A_{7} & A_{8} \\
        \end{bmatrix},\quad

        \mathbb{B} =
        \begin{bmatrix}
        B_{0} & B_{1} & B_{2} \\
        B_{3} & B_{4} & B_{5} \\
        B_{6} & B_{7} & B_{8} \\
        \end{bmatrix},\quad

        \mathbb{C} =
        \begin{bmatrix}
        C_{0} & C_{1} & C_{2} \\
        C_{3} & C_{4} & C_{5} \\
        C_{6} & C_{7} & C_{8} \\
        \end{bmatrix},\quad

        \mathbb{D} =
        \begin{bmatrix}
        D_{0} & D_{1} & D_{2} \\
        D_{3} & D_{4} & D_{5} \\
        D_{6} & D_{7} & D_{8} \\
        \end{bmatrix},\quad

        \mathbb{E} =
        \begin{bmatrix}
        E_{0} & E_{1} & E_{2} \\
        E_{3} & E_{4} & E_{5} \\
        E_{6} & E_{7} & E_{8} \\
        \end{bmatrix},\quad

        \mathbb{F} =
        \begin{bmatrix}
        F_{0} & F_{1} & F_{2} \\
        F_{3} & F_{4} & F_{5} \\
        F_{6} & F_{7} & F_{8} \\
        \end{bmatrix},\quad
        $$
    </p>
    <p>
        根据H进制转换矩阵:
    </p>
    <p>
        $$
        \mathbb{[A B C D E F]}\mathbb{[A B C D E F]}^\top =
        \begin{bmatrix}
        \mathbb{A} & \mathbb{A} & \mathbb{D} & \mathbb{D} & \mathbb{B} & \mathbb{B} \\
        \mathbb{A} & \mathbb{A} & \mathbb{D} & \mathbb{D} & \mathbb{B} & \mathbb{B} \\
        \mathbb{A} & \mathbb{A} & \mathbb{D} & \mathbb{D} & \mathbb{B} & \mathbb{B} \\
        \mathbb{E} & \mathbb{E} & \mathbb{C} & \mathbb{C} & \mathbb{F} & \mathbb{F} \\
        \mathbb{E} & \mathbb{E} & \mathbb{C} & \mathbb{C} & \mathbb{F} & \mathbb{F} \\
        \mathbb{E} & \mathbb{E} & \mathbb{C} & \mathbb{C} & \mathbb{F} & \mathbb{F} \\
        \end{bmatrix}
        $$
    </p>

    <p>
        为书写及计算方便，约定
        <span>\( R[\setminus \mathbb{X}]_i \)</span>
        表示除矩阵\(\mathbb{X}\)外所有矩阵的第\(i\)行向量，
        <span>\( C[\setminus \mathbb{X}]_i \)</span>
        表示除矩阵\(\mathbb{X}\)外所有矩阵的第\(i\)列向量。例如：
        <span>\( R[\setminus \mathbb{B}]_3 = [A_5 &nbsp;A_6 &nbsp;A_7 &nbsp;C_5 &nbsp;C_6 &nbsp;C_7 &nbsp;D_5 &nbsp;D_6
            &nbsp;D_7 &nbsp;E_5 &nbsp;E_6 &nbsp;E_7 &nbsp;F_5 &nbsp;F_6 &nbsp;F_7] \)</span>
        ; <br>约定 <span>\( R[\setminus \mathbb{X_i}] \)</span>
        表示矩阵\(\mathbb{X}\)除元素\(X_i\)外该该行的所有其余元素，
        <span>\( C[\setminus \mathbb{X_i}] \)</span>
        表示矩阵\(\mathbb{X}\)除元素\(X_i\)外该该列的所有其余元素，例如：
        <span>\( C[\setminus \mathbb{B_2}] = [B_6 &nbsp;B_8]^\top \)</span>
    </p>
    <p>将所有三阶参数矩阵带入，最终可得54个方程的组。</p>
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